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Inverse Weighted Sparse Regularization and Its Application in Radon Transform.

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Title: Inverse Weighted Sparse Regularization and Its Application in Radon Transform.
Authors: Shi, Wei1 (AUTHOR), Li, Zhiwei2 (AUTHOR), Chen, Siyuan1,2 (AUTHOR), Wang, Ning2 (AUTHOR), Cheng, Ronghong1 (AUTHOR), Yang, Tonghe1 (AUTHOR)
Source: Remote Sensing. Jun2026, Vol. 18 Issue 11, p1834. 20p.
Subjects: Radon transforms, Compressed sensing, Imaging systems in seismology, Signal denoising, Mathematical regularization, Image reconstruction
Abstract: Highlights: What are the main findings? A data-driven inverse-weighted sparse regularization method is proposed for compressed sensing reconstruction, where transform domain coefficients are adaptively weighted based on the reciprocal of the data itself to protect effective signals while enhancing sparse constraints on noise and other irrelevant signals. Applied to the Radon transform in both time and frequency domains, the inverse-weighted strategy significantly improves reconstruction accuracy and noise suppression for both natural images and seismic data compared to common sparse constraints. What are the implications of the main findings? The adaptive inverse-weighting framework provides a flexible mechanism to enhance the ability of sparse constraints, enabling more robust recovery accuracy of compressive sensing algorithms for diverse data. Improved fidelity of sparse Radon transform reconstructions demonstrates practical benefits for seismic data processing and remote sensing image restoration, where protecting effective signals is critical for interpretation and analysis. In the reconstruction problem of compressed sensing, to address the challenge of adapting common sparse constraints to diverse data, we propose a data-driven inverse-weighted regularization for adaptive data matching to enhance the ability of sparse constraints. Specifically, we formulate a weighted regularization term based on the data transform domain, positing that higher values in the sparsity-promoting transform domain correspond to a greater probability of effective signals. Therefore, when solving sparse optimization problems, we inversely weight this portion based on the inverse relationship with the coefficient magnitude, thereby reducing its impact and mitigating damage to effective signals. However, recognizing that noise and other irrelevant signals are sparse and approximately uniformly distributed in the transform domain, we can increase the weight of this portion to boost the sparsity constraint in the transform domain, thereby enhancing noise suppression. Consequently, we presented the corresponding solution algorithm and convergence proof for inverse-weighted sparse regularization, along with an application example in the context of the Radon transform. Experimental data tests indicate that inverse-weighted sparse regularization enhances the capability of sparse constraints, protects effective signals, suppresses noise, and improves the recovery accuracy of compressive sensing algorithms, as demonstrated in natural image enhancement and seismic multiple suppression. [ABSTRACT FROM AUTHOR]
Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Inverse Weighted Sparse Regularization and Its Application in Radon Transform.
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  Data: <searchLink fieldCode="JN" term="%22Remote+Sensing%22">Remote Sensing</searchLink>. Jun2026, Vol. 18 Issue 11, p1834. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Radon+transforms%22">Radon transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Compressed+sensing%22">Compressed sensing</searchLink><br /><searchLink fieldCode="DE" term="%22Imaging+systems+in+seismology%22">Imaging systems in seismology</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+denoising%22">Signal denoising</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink><br /><searchLink fieldCode="DE" term="%22Image+reconstruction%22">Image reconstruction</searchLink>
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  Label: Abstract
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  Data: Highlights: What are the main findings? A data-driven inverse-weighted sparse regularization method is proposed for compressed sensing reconstruction, where transform domain coefficients are adaptively weighted based on the reciprocal of the data itself to protect effective signals while enhancing sparse constraints on noise and other irrelevant signals. Applied to the Radon transform in both time and frequency domains, the inverse-weighted strategy significantly improves reconstruction accuracy and noise suppression for both natural images and seismic data compared to common sparse constraints. What are the implications of the main findings? The adaptive inverse-weighting framework provides a flexible mechanism to enhance the ability of sparse constraints, enabling more robust recovery accuracy of compressive sensing algorithms for diverse data. Improved fidelity of sparse Radon transform reconstructions demonstrates practical benefits for seismic data processing and remote sensing image restoration, where protecting effective signals is critical for interpretation and analysis. In the reconstruction problem of compressed sensing, to address the challenge of adapting common sparse constraints to diverse data, we propose a data-driven inverse-weighted regularization for adaptive data matching to enhance the ability of sparse constraints. Specifically, we formulate a weighted regularization term based on the data transform domain, positing that higher values in the sparsity-promoting transform domain correspond to a greater probability of effective signals. Therefore, when solving sparse optimization problems, we inversely weight this portion based on the inverse relationship with the coefficient magnitude, thereby reducing its impact and mitigating damage to effective signals. However, recognizing that noise and other irrelevant signals are sparse and approximately uniformly distributed in the transform domain, we can increase the weight of this portion to boost the sparsity constraint in the transform domain, thereby enhancing noise suppression. Consequently, we presented the corresponding solution algorithm and convergence proof for inverse-weighted sparse regularization, along with an application example in the context of the Radon transform. Experimental data tests indicate that inverse-weighted sparse regularization enhances the capability of sparse constraints, protects effective signals, suppresses noise, and improves the recovery accuracy of compressive sensing algorithms, as demonstrated in natural image enhancement and seismic multiple suppression. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Radon transforms
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      – SubjectFull: Imaging systems in seismology
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      – SubjectFull: Signal denoising
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      – SubjectFull: Mathematical regularization
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      – SubjectFull: Image reconstruction
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      – TitleFull: Inverse Weighted Sparse Regularization and Its Application in Radon Transform.
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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